仅使用IEEE 754二进制浮点运算的改进模乘法算法

IF 5.4 2区 计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS
Yukimasa Sugizaki;Daisuke Takahashi
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引用次数: 0

摘要

在本文中,我们提出了三种仅使用IEEE 754二进制浮点运算的模块化乘法算法。以前的一些研究使用浮点运算来执行模乘法。然而,他们只考虑正整数,并且没有使用浮点表示中的专用符号位。我们的第一个算法是这些基于Shoup乘法的研究的扩展。通过允许操作数为负,我们将最大支持模量大小增加了约1.21倍。剩下的两个算法分别基于正整数和有符号整数的Montgomery乘法。尽管这些算法需要更多的从整数到整数的运算,但它们支持的模数大小是正整数的Shoup乘法的两倍。对于具有相对较低的舍入到整性能的处理器,我们提出了不进行舍入到整操作的三种算法版本。在四个具有不同指令性能水平的cpu上进行的评估表明,对于中等大小的模,基于浮点的算法(包括本文提出的算法)可以被视为基于整数的算法的替代方案,特别是当处理器上的浮点运算速度更快时。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Improved Modular Multiplication Algorithms Using Solely IEEE 754 Binary Floating-Point Operations
In this paper, we propose three modular multiplication algorithms that use only the IEEE 754 binary floating-point operations. Several previous studies have used floating-point operations to perform modular multiplication. However, they considered only positive integers and did not utilize the dedicated sign bit in the floating-point representation. Our first algorithm is an extension of these studies, which are based on Shoup multiplication. By allowing operands to be negative, we increased the maximum supported modulus size by approximately 1.21 times. Our remaining two algorithms are based on Montgomery multiplication for positive and signed integers, respectively. Although these algorithms require more round-to-integral operations, they support a modulus size of up to twice as large as that for Shoup multiplication for positive integers. For processors with relatively low round-to-integral performance, we propose versions of the three algorithms without the round-to-integral operation. Evaluations on four CPUs with different levels of instruction performance show that floating-point-based algorithms, including the proposed algorithms, can be regarded as alternatives to integer-based algorithms for mid-sized moduli, especially when floating-point operations are faster on the processors.
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来源期刊
IEEE Transactions on Emerging Topics in Computing
IEEE Transactions on Emerging Topics in Computing Computer Science-Computer Science (miscellaneous)
CiteScore
12.10
自引率
5.10%
发文量
113
期刊介绍: IEEE Transactions on Emerging Topics in Computing publishes papers on emerging aspects of computer science, computing technology, and computing applications not currently covered by other IEEE Computer Society Transactions. Some examples of emerging topics in computing include: IT for Green, Synthetic and organic computing structures and systems, Advanced analytics, Social/occupational computing, Location-based/client computer systems, Morphic computer design, Electronic game systems, & Health-care IT.
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